This work investigates and evaluates multiple defense strategies against property inference attacks (PIAs), a privacy attack against machine learning models. Given a trained machine learning model, PIAs aim to extract statistical properties of its underlying training data, e.g., reveal the ratio of men and women in a medical training data set. While for other privacy attacks like membership inference, a lot of research on defense mechanisms has been published, this is the first work focusing on defending against PIAs. With the primary goal of developing a generic mitigation strategy against white-box PIAs, we propose the novel approach property unlearning. Extensive experiments with property unlearning show that while it is very effective when defending target models against specific adversaries, property unlearning is not able to generalize, i.e., protect against a whole class of PIAs. To investigate the reasons behind this limitation, we present the results of experiments with the explainable AI tool LIME. They show how state-of-the-art property inference adversaries with the same objective focus on different parts of the target model. We further elaborate on this with a follow-up experiment, in which we use the visualization technique t-SNE to exhibit how severely statistical training data properties are manifested in machine learning models. Based on this, we develop the conjecture that post-training techniques like property unlearning might not suffice to provide the desirable generic protection against PIAs. As an alternative, we investigate the effects of simpler training data preprocessing methods like adding Gaussian noise to images of a training data set on the success rate of PIAs. We conclude with a discussion of the different defense approaches, summarize the lessons learned and provide directions for future work.

Attention to data-driven optimization approaches, including the well-known stochastic gradient descent method, has grown significantly over recent decades, but data-driven constraints have rarely been studied, because of the computational challenges of projections onto the feasible set defined by these hard constraints. In this paper, we focus on the non-smooth convex-concave stochastic minimax regime and formulate the data-driven constraints as expectation constraints. The minimax expectation constrained problem subsumes a broad class of real-world applications, including two-player zero-sum game and data-driven robust optimization. We propose a class of efficient primal-dual algorithms to tackle the minimax expectation-constrained problem, and show that our algorithms converge at the optimal rate of $\mathcal{O}(\frac{1}{\sqrt{N}})$. We demonstrate the practical efficiency of our algorithms by conducting numerical experiments on large-scale real-world applications.

Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor factorization, one of the most popular approaches is to employ simple iterative algorithms such as gradient descent (GD) to recover the low-rank factors directly, which allow for small memory and computation footprints. However, the convergence rate of GD depends linearly, and sometimes even quadratically, on the condition number of the low-rank object, and therefore, GD slows down painstakingly when the problem is ill-conditioned. This chapter introduces a new algorithmic approach, dubbed scaled gradient descent (ScaledGD), that provably converges linearly at a constant rate independent of the condition number of the low-rank object, while maintaining the low per-iteration cost of gradient descent for a variety of tasks including sensing, robust principal component analysis and completion. In addition, ScaledGD continues to admit fast global convergence to the minimax-optimal solution, again almost independent of the condition number, from a small random initialization when the rank is over-specified in the presence of Gaussian noise. In total, ScaledGD highlights the power of appropriate preconditioning in accelerating nonconvex statistical estimation, where the iteration-varying preconditioners promote desirable invariance properties of the trajectory with respect to the symmetry in low-rank factorization without hurting generalization.

However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and can not be adapted. Our goal is to allow flexible symmetry constraints that can automatically be learned from data using gradients. Learning symmetry and associated weight connectivity structures from scratch is difficult for two reasons. First, it requires efficient and flexible parameterisations of layer-wise equivariances. Secondly, symmetries act as constraints and are therefore not encouraged by training losses measuring data fit. To overcome these challenges, we improve parameterisations of soft equivariance and learn the amount of equivariance in layers by optimising the marginal likelihood, estimated using differentiable Laplace approximations. The objective balances data fit and model complexity enabling layer-wise symmetry discovery in deep networks. We demonstrate the ability to automatically learn layer-wise equivariances on image classification tasks, achieving equivalent or improved performance over baselines with hard-coded symmetry.

Support vector machines (SVMs) are widely used and constitute one of the best examined and used machine learning models for two-class classification. Classification in SVM is based on a score procedure, yielding a deterministic classification rule, which can be transformed into a probabilistic rule (as implemented in off-the-shelf SVM libraries), but is not probabilistic in nature. On the other hand, the tuning of the regularization parameters in SVM is known to imply a high computational effort and generates pieces of information that are not fully exploited, not being used to build a probabilistic classification rule. In this paper we propose a novel approach to generate probabilistic outputs for the SVM. The new method has the following three properties. First, it is designed to be cost-sensitive, and thus the different importance of sensitivity (or true positive rate, TPR) and specificity (true negative rate, TNR) is readily accommodated in the model. As a result, the model can deal with imbalanced datasets which are common in operational business problems as churn prediction or credit scoring. Second, the SVM is embedded in an ensemble method to improve its performance, making use of the valuable information generated in the parameters tuning process. Finally, the probabilities estimation is done via bootstrap estimates, avoiding the use of parametric models as competing approaches. Numerical tests on a wide range of datasets show the advantages of our approach over benchmark procedures.

Generative models, like large language models, are becoming increasingly relevant in our daily lives, yet a theoretical framework to assess their generalization behavior and uncertainty does not exist. Particularly, the problem of uncertainty estimation is commonly solved in an ad-hoc manner and task dependent. For example, natural language approaches cannot be transferred to image generation. In this paper we introduce the first bias-variance-covariance decomposition for kernel scores and their associated entropy. We propose unbiased and consistent estimators for each quantity which only require generated samples but not the underlying model itself. As an application, we offer a generalization evaluation of diffusion models and discover how mode collapse of minority groups is a contrary phenomenon to overfitting. Further, we demonstrate that variance and predictive kernel entropy are viable measures of uncertainty for image, audio, and language generation. Specifically, our approach for uncertainty estimation is more predictive of performance on CoQA and TriviaQA question answering datasets than existing baselines and can also be applied to closed-source models.

Modern machine learning methods and the availability of large-scale data opened the door to accurately predict target quantities from large sets of covariates. However, existing prediction methods can perform poorly when the training and testing data are different, especially in the presence of hidden confounding. While hidden confounding is well studied for causal effect estimation (e.g., instrumental variables), this is not the case for prediction tasks. This work aims to bridge this gap by addressing predictions under different training and testing distributions in the presence of unobserved confounding. In particular, we establish a novel connection between the field of distribution generalization from machine learning, and simultaneous equation models and control function from econometrics. Central to our contribution are simultaneous equation models for distribution generalization (SIMDGs) which describe the data-generating process under a set of distributional shifts. Within this framework, we propose a strong notion of invariance for a predictive model and compare it with existing (weaker) versions. Building on the control function approach from instrumental variable regression, we propose the boosted control function (BCF) as a target of inference and prove its ability to successfully predict even in intervened versions of the underlying SIMDG. We provide necessary and sufficient conditions for identifying the BCF and show that it is worst-case optimal. We introduce the ControlTwicing algorithm to estimate the BCF and analyze its predictive performance on simulated and real world data.

We consider a binary classification problem under group fairness constraints, which can be one of Demographic Parity (DP), Equalized Opportunity (EOp), or Equalized Odds (EO). We propose an explicit characterization of Bayes optimal classifier under the fairness constraints, which turns out to be a simple modification rule of the unconstrained classifier. Namely, we introduce a novel instancelevel measure of bias, which we call bias score, and the modification rule is a simple linear rule on top of the finite amount of bias scores. Based on this characterization, we develop a post-hoc approach that allows us to adapt to fairness constraints while maintaining high accuracy. In the case of DP and EOp constraints, the modification rule is thresholding a single bias score, while in the case of EO constraints we are required to fit a linear modification rule with 2 parameters. The method can also be applied for composite group-fairness criteria, such as ones involving several sensitive attributes. We achieve competitive or better performance compared to both in-processing and post-processing methods across three datasets: Adult, COMPAS, and CelebA. Unlike most post-processing methods, we do not require access to sensitive attributes during the inference time. Significant improvements have been made in classification tasks using machine learning (ML) algorithms. With ML algorithms being deployed in more and more decision-making applications, it is crucial to ensure fairness in their predictions. Although the debate on what is fairness and how to measure it is ongoing (Caton & Haas, 2023), oftentimes group fairness measures are utilized in practice due to the simplicity of their verification (Chouldechova, 2017; Hardt et al., 2016a), which conform to the intuition that predictions should not be biased toward a specific group of the population.

In this study, we propose a novel deep spatio-temporal point process model, Deep Kernel Mixture Point Processes (DKMPP), that incorporates multimodal covariate information. DKMPP is an enhanced version of Deep Mixture Point Processes (DMPP), which uses a more flexible deep kernel to model complex relationships between events and covariate data, improving the model's expressiveness. To address the intractable training procedure of DKMPP due to the non-integrable deep kernel, we utilize an integration-free method based on score matching, and further improve efficiency by adopting a scalable denoising score matching method. Our experiments demonstrate that DKMPP and its corresponding score-based estimators outperform baseline models, showcasing the advantages of incorporating covariate information, utilizing a deep kernel, and employing score-based estimators.

Bayesian deep learning counts on the quality of posterior distribution estimation. However, the posterior of deep neural networks is highly multi-modal in nature, with local modes exhibiting varying generalization performance. Given a practical budget, sampling from the original posterior can lead to suboptimal performance, as some samples may become trapped in "bad" modes and suffer from overfitting. Leveraging the observation that "good" modes with low generalization error often reside in flat basins of the energy landscape, we propose to bias sampling on the posterior toward these flat regions. Specifically, we introduce an auxiliary guiding variable, the stationary distribution of which resembles a smoothed posterior free from sharp modes, to lead the MCMC sampler to flat basins. By integrating this guiding variable with the model parameter, we create a simple joint distribution that enables efficient sampling with minimal computational overhead. We prove the convergence of our method and further show that it converges faster than several existing flatness-aware methods in the strongly convex setting. Empirical results demonstrate that our method can successfully sample from flat basins of the posterior, and outperforms all compared baselines on multiple benchmarks including classification, calibration, and out-of-distribution detection.